Question

Two magnets of magnetic moments $M$ and $\sqrt{3}M$ are joined to form a cross $(+)$. The combination is suspended freely in a uniform magnetic field. In equilibrium position the angle between the magnetic moment M and the field is:

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

The correct option is C ${60}^o$

Let the magnet having magnetic moment $M$ makes an angle $\theta$ with the magnetic field.
Then, the magnet having magnetic moment $\sqrt{3}M$ makes an angle $(90-\theta )$ with the magnetic field.
In equilibrium, both the torques are balanced.
$MB\sin \theta =\sqrt{3}MB\sin (90-\theta )=\sqrt{3}MB\cos \theta$
$\Rightarrow \tan \theta =\sqrt{3}=\tan {60}^{\circ }$
$\theta ={60}^{\circ }$